I had engineering tests as take-home before. It wasn't super common, but some professors did do that for seniors on occasion for small classes where cheating wouldn't be a problem. They were so stupidly hard that even with multiple text books and the internet, the best I could often do was a "B". There's simply no way to google an answer for something that requires multiple pages of analysis and so forth per problem. I think this was a fairer representation of the real world too.
I think a take home test would be harder for those subjects that are more about rote memorization.
My university had an interesting solution for a couple of modules for computer science - there were six programming assignments spread throughout the term, and you do them at home and submitted online. It'd be (obviously) very easy to cheat, and being programming a certain degree of similarity would be expected. However, for the final assignment, you had to go for a viva. You had to explain how it worked and why you'd chosen to do things in a certain way, and that formed the bulk of your assessment.
I think a take home test would be harder for those subjects that are more about rote memorization.